This booklet is intended for high-school students interested
in mathematics. It is concerned with approximating real
numbers by rational ones, which is one of the most captivating
topics in arithmetic.

â¦
Continued fractions represent one of the most perfect
creations of 17-18th century mathematicians: Huygens, Euler,
Lagrange, and Legendre. The properties of these fractions
are really striking.

The following should be borne in mind when reading this
booklet. Topics easily understandable are presented in normal print,
while those more difficult are given in small print. Proofs of some theorems given in small print may be omitted safely. These theorems will necessarily be taken for granted. However, mathematics is not just reading for entertainment. A future mathematician as well as a physicist or an engineer has to acquire skill in dealing with mathematical constructions and proofs. So take a pencil and a sheet of paper and study carefully the topics given in small print. You may succeed in simplifying some proofs or finding better ones.

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